scholarly journals On the cohomology of the mod-2 Steenrod algebra and the non-existence of elements of Hopf invariant one

1967 ◽  
Vol 11 (3) ◽  
pp. 480-490 ◽  
Author(s):  
John S. P. Wang
Keyword(s):  
Steenrod Algebra ◽  
Hopf Invariant

The smallest subgroup whose invariants are hit by the Steenrod algebra

2007 ◽  
Vol 142 (1) ◽  
pp. 63-71
Author(s):  
NGUYỄN H. V. HƯNG ◽  
TRAN DINH LUONG
Keyword(s):  
Vector Space ◽  
Polynomial Algebra ◽  
Steenrod Algebra ◽  
Vector Subspace ◽  
Dimensional Vector ◽  
Hopf Invariant ◽  
Algebraic Version

AbstractLet V be a k-dimensional ${\mathbb{F}_2}$-vector space and let W be an n-dimensional vector subspace of V. Denote by GL(n, ${\mathbb{F}_2}$) • 1k-n the subgroup of GL(V) consisting of all isomorphisms ϕ:V → V with ϕ(W) = W and ϕ(v) ≡ v (mod W) for every v ∈ V. We show that GL(3, ${\mathbb{F}_2}$) • 1k-3 is, in some sense, the smallest subgroup of GL(V)≅ GL(k, ${\mathbb{F}_2})$, whose invariants are hit by the Steenrod algebra acting on the polynomial algebra, ${\mathbb{F}_2})\cong{\mathbb{F}_2}[x_{1},\ldots,x_{k}]$. The result is some aspect of an algebraic version of the classical conjecture that the only spherical classes inQ0S0are the elements of Hopf invariant one and those of Kervaire invariant one.

Polynomials and the mod 2 Steenrod Algebra

2017 ◽  
Author(s):  
Grant Walker ◽  
Reginald M. W. Wood
Keyword(s):  
Steenrod Algebra

Polynomials and the mod 2 Steenrod Algebra

2017 ◽  
Author(s):  
Grant Walker ◽  
Reginald M. W. Wood
Keyword(s):  
Steenrod Algebra

A Note on Parabolic Subgroups and the Steenrod Algebra Action

2008 ◽  
Vol 15 (04) ◽  
pp. 689-698
Author(s):  
Nondas E. Kechagias
Keyword(s):  
Steenrod Algebra ◽  
Parabolic Subgroups ◽  
Generating Set ◽  
Modular Invariants ◽  
Dickson Algebra

The ring of modular invariants of parabolic subgroups has been described by Kuhn and Mitchell using Dickson algebra generators. We provide a new generating set which is closed under the Steenrod algebra action along with the relations between these elements.

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